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Measurement, STD2 EQ-Bank 21

The distance between planets is measured in Astronomical Units (AU).

\(1\ \text{AU}\ \approx 1.496\times 10^8\) kilometres.

Given Venus is approximately 0.7 AU from Earth, calculate this distance in kilometres giving your answer in scientific notation, correct to 3 significant figures.   (2 marks)

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\(1.03\times 10^8\ \text{(3 sig. fig.)}\)

Show Worked Solution
\(\text{Distance}\) \(=0.7\times \left(1.496\times 10^8\right)\)
  \(=102\,830\,000\)
  \(=1.0283\times 10^8\)
  \(=1.03\times 10^8\ \text{(3 sig. fig.)}\)

Measurement, STD2 EQ-Bank 5 MC

The distance from the earth to the sun is approximately 150 million kilometres.

This distance expressed in scientific notation is:

  1. \(1.5\times 10^{9}\)
  2. \(1.5\times 10^{8}\)
  3. \(1.5\times 10^{7}\)
  4. \(1.5\times 10^{6}\)
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\(B\)

Show Worked Solution

\(150\ \text{million}\ =\ 150\,000\,000=1.5\times 10^8\)

\(\Rightarrow B\)

Measurement, STD2 EQ-Bank 2 MC

Arrange the numbers \(5.6\times 10^{-2}\), \(4.8\times 10^{-1}\), \(7.2\times 10^{-2}\) from smallest to largest.

  1. \(5.6\times 10^{-2}\),  \(7.2\times 10^{-2}\),  \(4.8\times 10^{-1}\)
  2. \(4.8\times 10^{-1}\),  \(5.6\times 10^{-2}\),  \(7.2\times 10^{-2}\)
  3. \(7.2\times 10^{-2}\),  \(5.6\times 10^{-2}\),  \(4.8\times 10^{-1}\)
  4. \(4.8\times 10^{-1}\),  \(7.2\times 10^{-2}\),  \(5.6\times 10^{-2}\)
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\(A\)

Show Worked Solution

\(5.6\times 10^{-2}=0.052\)

\(4.8\times 10^{-1}=0.48\)

\(7.2\times 10^{-2}=0.072\)

\(\therefore\ \text{Correct order is: }\ 5.6\times 10^{-2}\),  \(7.2\times 10^{-2}\),  \(4.8\times 10^{-1}\)

\(\Rightarrow A\)

Measurement, STD1 M1 2025 HSC 4 MC

What is \(6\ 280\ 000\) in standard form?

  1. \(628\times 10^4\)
  2. \(62.8\times 10^5\)
  3. \(6.28\times 10^6\)
  4. \(0.628\times 10^7\)
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\(C\)

Show Worked Solution

\(6\ 280\ 000=6.28\times 10^6\)

\(\Rightarrow C\)


♦♦♦ Mean mark 29%.

Measurement, STD1 M1 2022 HSC 4 MC

The area `(A)` of a circle is given by the formula `A=\pi r^2`, where `r` is the radius.

What is the value of `A`, correct to three significant figures, if `r=3.55` ?

  1. 39.5
  2. 39.6
  3. 39.591
  4. 39.592
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`B`

Show Worked Solution
`A` `=pi\r^2`  
  `=pi xx3.55^2`  
  `=39.591…`  
  `=39.6\ \ text{(3 sig fig)}`  

  
`=>B`


♦♦ Mean mark 30%.
COMMENT: Significant figures warrant attention.

Measurement, STD1 M1 2020 HSC 3 MC

What is 0.002073 expressed in standard form with two significant figures?

  1. `2.07 xx 10^(-2)`
  2. `2.1 xx 10^(-2)`
  3. `2.07 xx 10^(-3)`
  4. `2.1 xx 10^(-3)`
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`B`

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♦♦♦ Mean mark 12%.
`0.002073` `= 2.073 xx 10^(-3)`  
  `=2.1 xx 10^(-3)\ \ \ text{(to 2 sig fig)}`  

 
`=> B`

Measurement, STD2 M1 2020 HSC 2 MC

What is 0.002073 expressed in standard form with two significant figures?

  1. `2.07 xx 10^(-2)`
  2. `2.1 xx 10^(-2)`
  3. `2.07 xx 10^(-3)`
  4. `2.1 xx 10^(-3)`
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`D`

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♦♦ Mean mark 35%.
COMMENT: A notable knowledge gap flagged by this result.
`0.002073` `= 2.073 xx 10^(-3)`  
  `=2.1 xx 10^(-3)\ \ \ text{(to 2 sig fig)}`  

 
`=> D`

Measurement, STD2 M1 2016 HSC 1 MC

What is  208.345  correct to two significant figures?

  1. 208
  2. 210
  3. 208.34
  4. 208.35
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`B`

Show Worked Solution

`208.345 = 210\ (2\ text(sig. fig.))`

♦♦ Mean mark 36%!!

`=> B`

 

Measurement, STD2 M1 2015 HSC 1 MC

What is  1 560 200 km written in standard form correct to two significant figures?

  1. `1.56 × 10^4 \ text(km)`
  2. `1.6 × 10^5 \ text(km)`
  3. `1.56 × 10^6 \ text(km)`
  4. `1.6 × 10^6 \ text(km)`
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`D`

Show Worked Solution

♦♦ Mean mark 30%.
COMMENT: Incredibly, the first MC question in 2015 had the lowest mean mark of all MC questions in the exam!

`1\ 560\ 200`

`= 1.5602 xx 10^6`

`= 1.6 xx 10^6\ text(km)\ \ \ text{(2 sig fig)}`

 
`=> D`

Measurement, STD2 M1 2004 HSC 13 MC

During a ten-minute period, Kath is exercising and Jim is resting.

How much more air would Kath breathe than Jim during this time?

  1.  40 Litres
  2. 94 Litres
  3. 940 Litres
  4. 1060 Litres
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`C`

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`text(Kath’s air volume)`

`= 10 xx 100`

`=1000\ text(L)`

`text(Jim’s air volume)`

`= 10 xx 6`

`= 60\text(L)`
 

`:.\ text(Extra air that Kath breathes)`

`= 1000 – 60`

`= 940\ text(L)`

`=>  C`

Measurement, STD2 M1 2007 HSC 1 MC

What is  `0.000\ 000\ 326`  mm expressed in scientific notation?

  1. `0.326 xx 10^-6\ \ text(mm)`
  2. `3.26 xx 10^-7\ \ text(mm)`
  3. `0.326 xx 10^6\ \ text(mm)`
  4. `3.26 xx 10^7\ \ text(mm)`
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`B`

Show Worked Solution

`0.000\ 000\ 326\ text(mm)`

`= 3.26 xx 10^-7\ \ text(mm)`

`=> B`

Measurement, STD2 M1 2014 HSC 2 MC

A measurement of  72 cm is increased by 20% and then the result is decreased by 20%. 

What is the new measurement, correct to the nearest centimetre?

  1. 46 cm
  2. 69 cm
  3. 72 cm
  4. 104 cm
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`B`

Show Worked Solution
STRATEGY: Students confident in this area could save time in the calculations as follows: `72 xx 1.2 xx 0.8“ = 69.12`

`text(72 increased by 20%)`

`= 72 + (text(20%) xx 72) = 86.4\ text(cm)`

`text(86.4 decreased by 20%)`

`= 86.4\ – (text(20%) xx 86.4) = 69.12\ text(cm)`

`=>  B`

Measurement, STD2 M1 2009 HSC 12 MC

How many square centimetres are in 0.0075 square metres? 

  1. 0.75 
  2. 7.5 
  3. 75
  4. 7500
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`C`

Show Worked Solution
`text{Since 1 m}^2` `= 100\ text(cm) xx 100\ text(cm)`
  `= 10\ 000\ text{cm}^2`

 

♦♦♦ Mean mark 19%.
`:.0.0075\ text{m}^2`  `= 0.0075 xx 10\ 000`
  `= 75\ text{cm}^2`

`=>  C`

Measurement, STD2 M1 2012 HSC 26g

Bhawana purchases pool chlorine in a new container which holds 35 kg.
 

2012 26g

 
She begins using this new container on the first day of a week.

How many full weeks should this container last?     (2 marks)

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 `text(15 full weeks.)`

Show Worked Solution
`text(Cups used per week)` `= 3 + 6 = 9`
`text(Chlorine usage per week)` `= 9 xx 250text(g)`
  `= 2250 text(g)`

 
`text(Total chlorine available)\ = 35text(kg) = 35\ 000\  text(grams)`

MARKER’S COMMENT: Better answers converted all measurements to grams (rather than use decimals and kgs) and realised the answer should be in full weeks.
`text(Time it will last)` `= (35\ 000)/2250`
  `= 15.555…`

 

`:.\ text(The container will last 15 full weeks.)`